12.1.2017

We invite you to the seminar of the Department of Theoretical Methods entitled Fitting conics and quadric surfaces to correlated data that will take place on Tuesday, January 17 at 10:00 a.m. in the Institute of Measurement Science SAS. The lecturer will be doc. RNDr. Eva Fišerová Ph.D. from the Department of Mathematical Analysis and Mathematics Applications of the Faculty of Natural Sciences, Palacky University in Olomouc, Czech Republic. 

Fitting conics and quadric surfaces to correlated data

Eva Fišerová

Palacký University in Olomouc, Czech Republic 

Fitting quadratic curves and quadratic surfaces to given data points is a fundamental task in many fields like engineering, astronomy, physics, biology, quality control, image processing, etc. The classical approach for fitting is geometric fit based on minimization of geometric distances from observed data points to the fitted curve/surface. In the lecture, we focus on solving the problem of geometric fit to correlated data using the linear regression model with nonlinear constraints. The constraints are represented by the general equation of the certain curve/surface. In order to obtain approximate linear regression model, these nonlinear constraints are being linearized by the first-order Taylor expansion. The iterative estimation procedure provides locally best linear unbiased estimates of the unknown algebraic parameters of the considered curve/surface together with unbiased estimates of variance components. Consequently, estimates of geometric parameters, volume, surface area, etc. and their uncertainties can be determined.

References

1. Chernov, N. (2010). Circular and Linear Regression: Fitting Circles and Lines by Least Squares. Chapman & Hall / CRC.
2. Koning, R., Wimmer, G., Witkovsky, V. (2014). Ellipse fitting by linearized nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase. Meas. Sci. Technol. 25, 115001.
3. Rao, C.R., Kleffe, J. (1988). Estimation of Variance Components and Applications. North- Holland, Amsterdam-Oxford-New York-Tokyo.